I'm familiar with the ideal gas law $$PV=nRT$$ but I don't think it applies to liquids like water. If I'm wrong, please correct me! If I'm right, then what equation of state applies to liquids such as water?

4 Answers
4

For all intents and purposes, you can use an incompressible equation of state:

$$ V = constant $$

That's it. No matter what pressure and temperature, you have the same volume. It's not completely true, but in relation to gasses it is true enough to make it that pressure work is negligible in liquids compared to gasses, and for liquids, you can just deal with the heat content without considering any work done in the expansions and contractions required to change temperature.

what about change in volume with temprature?
–
PrathyushOct 13 '12 at 12:26

That makes a lot of sense. In this case, does the equation of state remain as the ideal gas law?
–
PaulOct 13 '12 at 13:06

1

@Prathyush: no change in volume with either temperature or pressure--- this is the approximation which works for 99% of heat engines. You only have non-negligible volume changes in gasses. The reason is that liquids have touching atoms, and don't compress or decompress well. They do compress a little bit, but this is not a significant amount of work during heating and cooling cycles, or pressure increase/decrease cycles. It's not like in gasses, where the work and the heat are always comparable.
–
Ron MaimonOct 13 '12 at 15:28

@Paul: The equation of state is what I said V=constant, no dependence of V on P or T. So for this description, you need a Gibbs ensemble, P and T are independently varied and V is constant. If you use another ensemble and want to take the constant V limit, you have to give V a tiny dependence on pressure/temperature.
–
Ron MaimonOct 13 '12 at 15:30

@RonMaimon: Ok... I think I understand now... If the fluid is incompressible, then pressure and temperature do not affect the volume occupied by a constant quanitity of mass. Compressibility necessarily implies that pressure and temperature affect the volume occupied by a constant quanitity of mass. Am I stating this correctly?
–
PaulOct 13 '12 at 16:04

Accurate equations of states (EOS) for real gases, liquids, or solids are (in contrast to nice theoretical models such as an ideal gas or debye solid) quite complex, and must be fitted to experimental data.

For example, a very accurate equation of state for water and steam can be found in
Wagner and Pruss,
The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use, 1995http://www.teos-10.org/pubs/Wagner_and_Pruss_2002.pdf